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Limitative computational explanations

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Abstract

What is computational explanation? Many accounts treat it as a kind of causal explanation. I argue against two more specific versions of this view, corresponding to two popular treatments of causal explanation. The first holds that computational explanation is mechanistic, while the second holds that it is interventionist. However, both overlook an important class of computational explanations, which I call limitative explanations. Limitative explanations explain why certain problems cannot be solved computationally, either in principle or in practice. I argue that limitative explanations are not plausibly understood in either mechanistic or interventionist terms. One upshot of this argument is that there are causal and non-causal kinds of computational explanation. I close the paper by suggesting that both are grounded in the notion of computational implementation.

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Notes

  1. In computer security, the branch of computer science that studies malware, it is standard to distinguish worms from viruses. Worms introduce new, potentially malicious programs into a filesystem; viruses inject potentially malicious code into pre-existing programs or files. The love bug was actually something of a hybrid, since it infected pre-existing files as well as introducing new, malicious files of its own.

  2. For an informal proof for the case of viruses in particular, see (Cohen, 1987). (Cohen, 1989) is a more technical treatment.

  3. I will move back and forth between talking about computational models as classes of mathematical objects and as members of such a class. Thus, for instance, I will sometimes talk of the Turing machine model M, and other times I will talk of a particular Turing machine model m, where m ∊ M.

  4. Ordinarily this is taken to involve a degree of structural similarity (e.g., some sort of morphism between the computational features of the system and those of the model). It is controversial whether more than this is required; see (Piccinini & Maley 2021; Ritchie & Piccinini, 2019).

  5. A bit more precisely, under appropriate idealizations it implements a Turing-equivalent model. Two computational models are equivalent just in case each can simulate the other. Equivalent models can solve exactly the same computational problems. A model is Turing-equivalent just in case it is equivalent to a Turing machine. Turing-equivalent models can solve exactly those problems solvable by a Turing machine. For more on the relevant idealizations, see (Curtis-Trudel 2023).

  6. Subject to the following subtlety: the system in question cannot compute the problem in question qua computational model of a certain sort. This does not prevent it from computing the problem in some other way, unrelated to its status as a computational model of that sort.

  7. Thanks to an anonymous referee for encouraging me to clarify the structure of the dialectic.

  8. The new mechanism literature is large and growing. For entry points, see (Bechtel & Abrahamsen, 2005; Craver & Tabery, 2019; Glennan, 2017; Machamer et al., 2000).

  9. See (Coelho Mollo, 2018; Dewhurst, 2018; Fresco, 2021; Milkowski, 2013; Piccinini 2015, 2020).

  10. See e.g. (Cummins, 1983, p. 29). However, Piccinini and Craver (2011) argue that functional analyses are mechanism sketches. See (Shapiro, 2017) for critical discussion. As should be clear, my argument does not depend on how this particular debate shakes out.

  11. For example, of the sort advanced by Lewis (1973) or Skow (2014). For Skow, one need merely provide information about causes, but need not represent causes.

  12. Rescorla (2014a) comes close, arguing that interventionism is appropriate for understanding the causal role of content in computational explanation. He does not, however, use the interventionist framework to develop a general theory of computational explanation. See also (Rescorla 2018) for an interventionist approach to explanation in Bayesian perceptual psychology.

  13. Of course, I do not claim that this exhausts the explanatory import of Marrian function-theoretic explanations. Rather, I claim only that the causal aspects of such explanations are naturally captured in interventionist terms. For more on function-theoretic explanations, see, e.g., (Egan, 2017; Shagrir, 2010).

  14. This is presumably the case in the actual world. Strictly speaking, since they have only finite memory, digital computers implement bounded-tape Turing machines. They implement full-strength Turing machines only under the idealization of unbounded memory.

  15. In offering a ‘unified’ account, I do not claim that a single, common factor makes non-causal and causal computational explanations explanatory. That is, I am not endorsing or offering a monistic account of explanation (Povich 2021; Reutlinger, 2016). Neither, by the same token, am I endorsing explanatory pluralism (Pincock, 2018). Rather, I aim to understand the sense in which both kinds of explanations are computational.

References

  • Appel, A. W., & Palsberg, J. (2002). Modern compiler implementation in Java. Cambridge University Press.

    Book  Google Scholar 

  • Attiya, H., & Ellen, F. (2014). Impossibility results for distributed computing. Morgan & Claypool.

    Book  Google Scholar 

  • Baker, A. (2005). Are there genuine mathematical explanations of physical phenomena? Mind, 114(454), 223–238.

    Article  Google Scholar 

  • Baron, S. (2019). Mathematical explanation by law. The British Journal for the Philosophy of Science, 70(3), 683–717.

    Article  Google Scholar 

  • Bechtel, W., & Abrahamsen, A. (2005). Explanation: A mechanist alternative. Studies in History and Philosophy of Science Part c: Studies in History and Philosophy of Biological and Biomedical Sciences, 36(2), 421–441.

    Article  Google Scholar 

  • Button, T. (2009). SAD computers and two versions of the Church-–Turing thesis. The British Journal for the Philosophy of Science, 60(4), 765–792.

    Article  Google Scholar 

  • Coelho Mollo, D. (2018). Functional individuation, mechanistic implementation: The proper way of seeing the mechanistic view of concrete computation. Synthese, 195(8), 3477–3497.

    Article  Google Scholar 

  • Cohen, F. (1987). Computer viruses. Computers & Security, 6(1), 22–35.

    Article  Google Scholar 

  • Cohen, F. (1989). Computational aspects of computer viruses. Computers & Security, 8(4), 297–298.

    Article  Google Scholar 

  • Copeland, B. J. (2002). Accelerating Turing machines. Minds and Machines, 12(2), 281–301.

    Article  Google Scholar 

  • Copeland, B. J., & Sylvan, R. (1999). Beyond the universal Turing machine. Australasian Journal of Philosophy, 77(1), 46–66.

    Article  Google Scholar 

  • Craver, C., & Kaplan, D. (2020). Are more details better? On the norms of completeness for mechanistic explanations. The British Journal for the Philosophy of Science, 71(1), 287–319.

    Article  Google Scholar 

  • Craver, C., & Tabery, J. (2019). Mechanisms in science. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (summer 2019). Metaphysics Research Lab, Stanford University.

    Google Scholar 

  • Cummins, R. (1983). The nature of psychological explanation. MIT Press.

    Google Scholar 

  • Curtis-Trudel, A. (2023). Mathematical explanation in computer science. Philosophy of Science, 1–10. https://doi.org/10.1017/psa.2023.26

  • Dewhurst, J. (2018). Computing mechanisms without proper functions. Minds and Machines, 28(3), 569–588.

    Article  Google Scholar 

  • Earman, J., & Norton, J. D. (1993). Forever is a day: Supertasks in Pitowsky and Malament–Hogarth spacetimes. Philosophy of Science, 60(1), 22–42.

    Article  Google Scholar 

  • Egan, F. (2017). Function-theoretic explanation and the search for neural mechanisms. In D. M. Kaplan (Ed.), Explanation and integration in mind and brain science (pp. 145–163). Oxford University Press.

    Google Scholar 

  • Fodor, J. A. (1965). Explanations in psychology. In M. Black (Ed.), Philosophy in America (pp. 161–179). Cornell University Press.

    Google Scholar 

  • Fresco, N. (2021). Long-arm functional individuation of computation. Synthese, 199(5–6), 13993–14016.

    Article  Google Scholar 

  • Furnell, S. (2020). Getting Bitten by the love bug. ITNOW, 62(3), 38–39.

    Google Scholar 

  • Glennan, S. (2017). The new mechanical philosophy. Oxford University Press.

    Book  Google Scholar 

  • Hamkins, J. D., & Lewis, A. (2000). Infinite time Turing machines. Journal of Symbolic Logic, 65(2), 567–604.

    Article  Google Scholar 

  • Hogarth, M. (1994). Non-Turing computers and Non-Turing computability. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1994(1), 126–138.

    Google Scholar 

  • Hogarth, M. (2004). Deciding arithmetic using SAD computers. The British Journal for the Philosophy of Science, 55(4), 681–691.

    Article  Google Scholar 

  • Hogarth, M. (2009). Non-Turing computers are the new Non-Euclidean geometries. International Journal of Unconventional Computing, 5, 277–297.

    Google Scholar 

  • Hughes, J. F. (2014). Computer graphics: Principles and practice (3rd ed.). Addison-Wesley.

    Google Scholar 

  • Kaplan, D. M. (2011). Explanation and description in computational neuroscience. Synthese, 183(3), 339–373.

    Article  Google Scholar 

  • Knuth, D. (1998). The art of computer programming: Vol. 3: Sorting and searching (2nd ed.). Addison-Wesley.

    Google Scholar 

  • Lange, M. (2013). What makes a scientific explanation distinctively mathematical? The British Journal for the Philosophy of Science, 64(3), 485–511.

    Article  Google Scholar 

  • Lange, M. (2017). Because without cause: Non-causal explanations in science and mathematics. Oxford University Press.

    Google Scholar 

  • Lewis, D. (1973). Causation. The Journal of Philosophy, 70, 556–567.

    Article  Google Scholar 

  • Machamer, P., Darden, L., & Craver, C. F. (2000). Thinking about mechanisms. Philosophy of Science, 67(1), 1–25.

    Article  Google Scholar 

  • Milkowski, M. (2013). Explaining the computational mind. MIT Press.

    Book  Google Scholar 

  • Minsky, M., & Papert, S. (1988). Perceptrons: An introduction to computational geometry. MIT Press.

    Google Scholar 

  • Papadimitriou, C. H. (1994). Computational complexity. Addison-Wesley.

    Google Scholar 

  • Piccinini, G. (2015). Physical computation: A mechanistic account. Oxford University Press.

    Book  Google Scholar 

  • Piccinini, G. (2020). Neurocognitive mechanisms: explaining biological cognition. Oxford University Press.

    Book  Google Scholar 

  • Piccinini, G., & Craver, C. (2011). Integrating psychology and neuroscience: Functional analyses as mechanism sketches. Synthese, 183(3), 283–311.

    Article  Google Scholar 

  • Piccinini, G., & Maley, C. (2021). Computation in Physical Systems. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (summer 2021). Metaphysics Research Lab, Stanford University.

    Google Scholar 

  • Pincock, C. (2018). Accommodating explanatory pluralism. In A. Reutlinger & J. Saatsi (Eds.), Explanation beyond causation: Philosophical perspectives on non-causal explanations (pp. 39–56). Oxford University Press.

    Google Scholar 

  • Pincock, C. (2023). Mathematics and explanation. Elements in the Philosophy of Mathematics. Cambridge: Cambridge University Press. https://doi.org/10.1017/9781009039154

  • Povich, M. (2021). The Narrow Ontic Counterfactual Account of Distinctively Mathematical Explanation. The British Journal for the Philosophy of Science, 72(2), 511–543. https://doi.org/10.1093/bjps/axz008

    Article  Google Scholar 

  • Rescorla, M. (2014a). The Causal Relevance of Content to Computation. Philosophy and Phenomenological Research, 88(1), 173–208.

    Article  Google Scholar 

  • Rescorla, M. (2014b). A theory of computational implementation. Synthese, 191(6), 1277–1307.

    Article  Google Scholar 

  • Rescorla, M. (2018). An interventionist approach to psychological explanation. Synthese, 195(5), 1909–1940. https://doi.org/10.1007/s11229-017-1553-2

    Article  Google Scholar 

  • Reutlinger, A. (2016). Is there a monist theory of causal and noncausal explanations? The counterfactual theory of scientific explanation. Philosophy of Science, 83(5), 733–745.

    Article  Google Scholar 

  • Ritchie, J. B., & Piccinini, G. (2019). Computational implementation. In M. Sprevak & M. Colombo (Eds.), Routledge handbook of the computational mind (pp. 192–204). Routledge.

    Google Scholar 

  • Sedgewick, R., & Flajolet, P. (2013). An introduction to the analysis of algorithms (2nd ed.). Addison-Wesley.

    Google Scholar 

  • Shagrir, O. (2010). Marr on computational-level theories. Philosophy of Science, 77(4), 477–500.

    Article  Google Scholar 

  • Shapiro, L. A. (2017). Mechanism or bust? Explanation in psychology. The British Journal for the Philosophy of Science, 68(4), 1037–1059.

    Article  Google Scholar 

  • Sipser, M. (2013). Introduction to the theory of computation. Cengage.

    Google Scholar 

  • Skow, B. (2014). Are there non-causal explanations (of particular events)? The British Journal for the Philosophy of Science, 65(3), 445–467.

    Article  Google Scholar 

  • Soare, R. I. (1996). Computability and recursion. Bulletin of Symbolic Logic, 2(03), 284–321.

    Article  Google Scholar 

  • Turing, A. M. (1939). Systems of logic based on ordinals. Proceedings of the London Mathematical Society, s2-45(1), 161–228.

    Article  Google Scholar 

  • Turing, A. (1936). On computable numbers, with an application to the entscheidungsproblem. Proceedings of the London Mathematical Society, 42(1), 230–265.

    Article  Google Scholar 

  • Woodward, J. (2003). Making things happen: A theory of causal explanation. Oxford University Press.

    Google Scholar 

  • Woodward, J. (2013). Mechanistic explanation: Its scope and limits. Aristotelian Society Supplementary, 87(1), 39–65.

    Article  Google Scholar 

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Acknowledgement

Thanks to Christopher Pincock, Darrell Rowbottom, Richard Samuels, Stewart Shapiro, and participants of the 2023 OSU/Maribor/Rijeka Philosophy Conference for helpful comments and discussion. Thanks especially to two anonymous referees for their helpful feedback on an earlier version of this article.

Funding

The work described in this paper was partially supported by a Senior Research Fellowship award from the Research Grants Council of the Hong Kong SAR, China (‘Philosophy of Contemporary and Future Science’, Project no. SRFS2122-3H01).

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  1. Department of Philosophy, Lingnan University, Tuen Mun, Hong Kong SAR, China

    André Curtis-Trudel

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Curtis-Trudel, A. Limitative computational explanations. Philos Stud 180, 3441–3461 (2023). https://doi.org/10.1007/s11098-023-02039-w

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